Moving webs, particularly webs which are comparatively wide, have a tendency to uneven lateral stretch; sometimes the edge regions may curl slightly or, at the other times, the center regions may be slightly wavy or undulating. It has previously been proposed to provide for transverse stretching of such a moving web by positioning a transverse stretching roller in the path of the web. The transverse stretching roller is bent or bowed transversely to the moving direction of the web. Such a roller is a composite element formed of a plurality of roller elements, so that the degree of bending or bowing of the overall roller can be individually adjusted by adjusting the individual roller elements with respect to each other - see, for example, German Pat. No. 21 39 159. A roller construction of this type is a complex apparatus, and substantial mechanical equipment and linkages are necessary to permit the adjustment of the bending or bowing of the roller for effective stretching of the web, selectively at a central portion or at the edge portions.